Model-based meta-analysis of HbA1c reduction across SGLT2 inhibitors using dose adjusted by urinary glucose excretion

Abstract

This study was aimed to evaluate whether the dose–response relationship of the sodium glucose co-transporter-2 inhibitors (SGLT2is) in patients with type 2 diabetes mellitus (T2DM)—canagliflozin, dapagliflozin, empagliflozin, ipragliflozin, luseogliflozin, and tofogliflozin—can be explained in a unified manner based on their ability to promote urinary glucose excretion (UGE). Information on HbA1c reduction at various doses of each SGLT2i was collected from literatures on randomized controlled trials and was normalized based on the daily UGE data from phase I studies. After normalizing doses, the dose–response relationship of HbA1c reduction of most of SGLT2is was represented by a unified nonlinear mixed-effect model, with the estimated maximum HbA1c (%) reduction (E_max) of 0.796 points, whereas covariate analysis showed that canagliflozin had a 1.33-fold higher E_max than those of the other drugs. Other covariates included baseline HbA1c levels, body weight, disease duration, prior treatment, and renal function. Findings from this study would influence drug selection and adjustment in clinical practice. As with SGLT2is, in cases where the efficacy cannot be easily evaluated but an appropriate pharmacodynamic marker was assessed in early clinical trials, similar approaches for other drug classes can guide strategic and evidence-based dose selection in phase III trials.

Introduction

Type 2 diabetes mellitus (T2DM) is a disease in which chronic hyperglycemia persists because of inadequate insulin secretion and action^1,2. Sodium glucose co-transporter-2 inhibitors (SGLT2is) lower blood glucose levels in patients with T2DM by inhibiting glucose reabsorption in the kidneys and increasing urinary glucose excretion (UGE)³. In the proximal tubules of the kidney, SGLT2 is located upstream of sodium glucose co-transporter-1 (SGLT1) and is responsible for most of reabsorption. The contribution of SGLT1 and SGLT2 to glucose reabsorption depends on plasma glucose concentration and filtered glucose load; therefore, the relative contribution differs between healthy individuals and patients with T2DM, who tend to have high blood glucose levels and poor renal function⁴. However, based on the mechanism by which SGLT2i inhibits the transporter activity of SGLT2, the dose–response relationship of its UGE-promoting effect should be comparable between healthy individuals and patients with T2DM. Therefore, the dose-dependence of SGLT2i in promoting UGE in healthy individuals is expected to be consistent with its dose-dependent glucose-lowering effect in patients with T2DM. The aim of this study was to determine whether SGLT2is have a common mechanism in patients with T2DM based on the ‘dose-dependence of UGE-promoting effects in healthy individuals’.

Since the launch of dapagliflozin in 2012, many SGLT2is have been developed, with nine drugs currently available for T2DM: dapagliflozin, canagliflozin, ipragliflozin, tofogliflozin, luseogliflozin, empagliflozin, ertugliflozin, bexagliflozin, and sotagliflozin. The selectivity of SGLT2 for SGLT1 varies among these drugs, with sotagliflozin being the less selective (20-fold)⁵, followed by canagliflozin⁶ and ipragliflozin^7,8 (150 to 250-fold), whereas the others are selective for SGLT2 (approximately 1,000-fold)^9–12.

Differences in the efficacy and safety of these drugs are important clinical considerations^13–18. Shyangdan et al. performed a network meta-analysis of the efficacy of six SGLT2is at clinical doses in patients with T2DM and reported that 300 mg canagliflozin showed the strongest glucose lowering effect compared with those of other SGLT2 regimens¹⁷. In another study, Maloney et al. compared the efficacy of 24 anti-hyperglycemic drugs in patients with T2DM, including several drug classes other than SGLT2i, using a model-based meta-analysis approach. The results suggested that, similar to the aforementioned study, 300 mg of canagliflozin had the strongest glucose-lowering effect among SGLT2is¹⁸. Although these studies provided useful evidence for clinical decision-making, such as regarding treatment selection, whether the dose–response relationship for a specific SGLTi (e.g., canagliflozin) is superior to those of other drugs remains unclear. If differences exist in the dose–response relationships among SGLT2is, the factors explaining these differences is an important research question and may be useful for optimizing treatment with each drug.

To address these issues, we compare the dose–response (HbA1c change) relationships of different SGLT2is using a common model by applying the model-based meta-analysis (MBMA) approach to published clinical trial data for those SGLT2is. The dose used in each clinical trial was normalized using a “reference dose,” defined as the dose that provides the same UGE in healthy individuals. This dose was determined separately for each drug based on the dose-UGE relationship measured in the phase I clinical trials. Given that efficacy is examined using limited number of doses, it is difficult to precisely assess the dose–response relationship for a clinical endpoint with respect to a single drug. In contrast, our approach maximizes the information available for several different drugs in the same class, allowing for higher quality dose–response analysis. Based on the mechanism of action of SGLT2is, it is reasonable to normalize their doses based on the UGE.

This study provides insight into inter-drug differences in the HbA1c-lowering effects of SGLT2is in patients with T2DM and may contribute to improved clinical decision-making through precise analysis of how the HbA1c-lowering effects of SGLT2is are affected by patient background, such as renal activity, diabetes period, treatment durations, and SGLT2i selection.

Result

Data characteristics

Of the nine SGLT2is currently approved worldwide, luseogliflozin, ertugliflozin and bexagliflozin were not included in the study because data on either HbA1c or UGE were not publicly available. Table 1 summarizes the characteristics of the six SGLT2is (canagliflozin, dapagliflozin, empagliflozin, ipragliflozin, luseogliflozin, and tofogliflozin) evaluated in this study. All six drugs are conjugated in the liver but are divided into two types: the conjugation occurred in its unchanged form or in the CYP metabolite. The rate-limiting step that causes the loss of efficacy in the two types is different. After a single fasting dose, tofogliflozin has the shortest elimination half-life, which is 5.4 h¹⁹ whereas those of ipragliflozin²⁰ or dapagliflozin²¹ were the longest at approximately 12 h. The selectivity of SGLT2 for SGLT1 also differed, showing a value of 4,829-fold for empagliflozin¹⁰ as the most selective drug compared with 158-fold for canagliflozin as the least selective drug⁶.

Table 1.

Characteristics of the six sodium glucose co-transporter-2 inhibitors.

Drugs	Countries or number of countries where approval has been obtained	Metabolism	t1/2 (h)	IC50		SGLT2 selectivity*2	Clinical dose
				SGLT2	SGLT1
Canagliflozin	82	Glucuronide conjugation	10.2	4.2	663	158	100 mg (300 mg*3)
Dapagliflozin	96	Glucuronide conjugation	12.1	1.12	1391	1242	5 mg 10 mg
Empagliflozin	109	Glucuronide conjugation	9.88	1.3	6278	4829	10 mg 25 mg
Ipragliflozin	South Korea, Japan	Glucuronide conjugation	11.7	7.38	1880	255	50 mg 100 mg
Luseogliflozin	Thailand, Malaysia, Japan	CYP	11.2	2.26	2900	1283	2.5 mg 5 mg
Tofogliflozin	Japan	CYP	5.29	14.5	8200	566	20 mg

*¹ Information as of October 2019. *² Calculated by dividing the IC₅₀ of SGLT1 by that of SGLT2. *³ The maximum clinical dose in Japan is 100 mg. Information on t_1/2 and IC₅₀ is provided in the package insert for each drug.

Information on the UGE was obtained from phase I single-dose study of each SGLT2is in healthy participants (Table S1). For all drugs, the UGE increased with increasing dosage, and was 70–80 g/day at the maximum dosage (Fig. 1). The UGE range at the clinical dose for each drug was 40–60 g/day, with a geometric mean of 51.4 g/day. Therefore, the dose of each drug at which the UGE reached 51.4 g/day was defined as the reference dose.

Fig. 1.

Urinary glucose excretion (UGE) in healthy participants during single-dose phase I studies with six sodium glucose co-transporter-2 (SGLT2) inhibitors. UGE (g/day) indicates urinary glucose excretion at 24 h after drug administration; each data set is the mean value per dose group; colored circle plots indicate clinical doses. If there were no measured values of UGE at the clinical doses, the values were calculated from the regression equation and shown as a colored plot with an open circle. The geometric mean UGE for the six drugs is 51.4 [g/day]. The dotted line shows the reference dose [mg] of each drug, which is the dose at which UGE is 51.4 g/day.

A PubMed literature search yielded 137 studies. Among them, 83 studies with available data that met the criteria were included in this analysis (Fig. 2, Supplementary Table S2, and Supplementary File 1). Moreover, 17, 29, 22, seven, five, and three studies focused on canagliflozin, dapagliflozin, empagliflozin, ipragliflozin, luseogliflozin, and tofogliflozin, respectively. Most studies of canagliflozin, dapagliflozin, and empagliflozin, which are widely approved overseas, were conducted outside of Japan, whereas other drugs were studied in Japan (Supplementary Table S2).

Fig. 2.

Workflow of data collection for clinical studies on urinary glucose excretion (UGE) dose–response and HbA1c dose–response for sodium glucose co-transporter-2 inhibitors.

Dose normalization with UGE

After dose normalization, the relationship between the UGE and normalized doses of the six drugs was well explained by the linear-logarithmic model (passing through the point of 51.4 g/day UGE when the normalized dose was 1.0; Fig. 3). The normalized doses of tofogliflozin were relatively high, and the dynamic range of UGE tended to be smaller than those of the other drugs. In contrast, the normalized doses of ipragliflozin were relatively low.

Fig. 3.

Urinary glucose excretion (UGE) for six sodium glucose co-transporter-2 inhibitors versus normalized doses. Each line shows the mean (measured) daily glucose excretion for each dose group ± standard error and is color-coded according to the drug type. The solid black and gray lines represent the model curve and 95% confidence interval, respectively.

Modeling analysis

Figure 4 shows the measured HbA1c data from 83 studies on six SGLT2is and the estimated HbA1c change according to the UGE-normalized dose based on integrated analysis of the six drugs. The vertical axis represents the change in HbA1c from baseline, and the horizontal axis represents the normalized dose, which is the actual dose divided by the reference dose, where 1.0 is the dose at UGE = 51.4 g/day. The relationship between HbA1c changes and the normalized dose was mostly consistent among the six drugs.

Fig. 4.

Relationship between normalized dose and HbA1c change in patients with type 2 diabetes in phase II and III trials of six sodium glucose co-transporter-2 inhibitors. Each plot shows the HbA1c change from baseline (absolute value of the difference before and after treatment) for each panel. The solid black line and gray area are the population estimates and bootstrap 95% confidence intervals, respectively.

The parameter estimates and inter-study variability (ISV) in the final model are listed in Table 2A. The estimated HbA1c change at the normalized dose = 1.0 was − 0.692%.

Table 2.

Parameters estimates and covariates identified using stepwise method.

(A) Parameter estimates and inter-study variabilities (ISV) in the final model
Parameter	Estimate (bootstrap 95% CI)	ISV (ω)
Base [%]	− 0.124 (− 0.170 to − 0.0718)	0.191
Emax [%]	− 0.796 (− 1.17 to − 0.689)	0.214
Correlation coefficient of Base and Emax	–	0.785
ED50	0.251 (0.191 to 1.09)	–
n	0.662 (0.388 to 0.981)	–

(B) Covariates identified using stepwise method
Parameter	COV	COV range	f(COV)	f(COV) range
Emax	Baseline HbA1c [mg dL−1]	7.2–9.1	$e^{0.438(COV-8)}$	0.704–1.62
Emax	Body weight [kg]	61.0–96.7	${(COV/81.6)}^{-0.661}$	1.21–0.894
Emax	Canagliflozin	–	$Cana:1.33;Ot\text{h}ers:1$	–
Emax	GFR [mL min−1 1.73 m−2]	38.5–154.5	${(COV/85.9)}^{0.821}$	0.517–1.62
Emax	Pre-treatment	–	$Yes:1;No:1.230$	–
Emax	Diabetic duration [years]	0.25–18.2	$1-0.025\left(C,O,V,-,6.6\right)$	1.16–0.71
Base	Concomitant medications	–	$Yes:0;No:0.156$	–

The baseline HbA1c level, body weight, disease duration, prior treatment, glomerular filtration rate (GFR), and canagliflozin were identified as significant covariates on E_max, while concomitant medication was on Base (Table 2B). The greater HbA1c-lowering effect was associated with high baseline HbA1c levels, low body weight, short disease duration, no prior treatment, and high GFR. The E_max with canagliflozin treatment was 1.33-fold higher than those of the other drugs (Table 2B, Fig. 5). Multicollinearity between the selected covariates was addressed by checking the correlation between the variables a posteriori. The absolute value of the correlation coefficient was at most 0.23 (between baseline HbA1c level and duration of disease), showing no significant multicollinearity.

Fig. 5.

Comparison of the estimation results of canagliflozin and other drugs. Each solid line and its area are population estimates and bootstrap 95% confidence intervals (purple: canagliflozin, gray: other five drugs).

The model validity was visually evaluated using six types of goodness-of-fit plots (Fig. 6). Compared with the plot of observed data versus population predictions (Fig. 6a), the plot of observed data versus individual predictions (Fig. 6b) showed less variation. Furthermore, the conditional weighted residuals (CWRES) followed a normal distribution (Fig. 6c, f) and was unbiased for individual predictions (Fig. 6d) and normalized doses (Fig. 6e). The estimation results for each parameter and covariate agreed well with the original estimation results, except for the 50% E_max dose (ED₅₀); however, the 95% confidence interval (CI) appeared to be reliable (Supplementary Table S3).

Fig. 6.

Goodness-of-fit of the model to the data. Observations vs population predictions (a), observations vs individual predictions (b), square root of absolute value of conditional weighted residuals (CWRES) vs individual predictions (d), CWRES vs normalized dose (e), histogram for CWRES (c), and QQ plot for CQRES (f).

Discussion

MBMA was conducted using aggregated clinical trial data from six SGLT2is. To enable the dose-HbA1c change relationship of different SGLT2is to be explained and compared using the same model, the dose in each trial was normalized to a reference dose determined for each drug (i.e., dose that achieved the same UGE). In addition, we applied a nonlinear mixed-effects model that accounted for ISV to examine the impact of differences in study design, including the patient background and type of SGLT2i tested, on the dose–response relationship.

It may be pointed out that our approach contradicts the knowledge that dose-UGE relationships differ between healthy individuals and patients with T2DM³. Indeed, previous studies reported that explaining this difference requires consideration of differences in fasting plasma glucose levels between these populations²² and differences in the contributions of SGLT1 and SGLT2 to renal glucose reabsorption⁴. However, the purpose of this study was not to propose a marker that bridges healthy individuals and patients, but rather to link and compare the glucose-lowering effects of multiple SGLT2is in patients with T2DM using the same model. Except for sotagliflozin, all SGLT2is show at least 100-fold higher selectivity for SGLT2 compared to SGLT1. In addition, the plasma concentrations of these SGLT2is at clinical doses (~ tens of nanomoles) were low compared with their Ki values for SGLT1. Taken together, even if there is a discrepancy in the dose-UGE relationship between healthy individuals and patients with T2DM, the extent of the change is likely similar among different SGLT2is, regardless of differences in the SGLT1/SGLT2 balance if the efficacy is derived from the drugs in the plasma. Thus, the validity of our approach for normalizing and comparing the dose–response relationship of each SGLT2is in patients with T2DM based on healthy human-derived UGE is not compromised by potential differences in the glucose regulatory systems between these patients and healthy individuals.

We conducted a bootstrap analysis to check stability of the model and found that the ED₅₀ was unstable. However, the Hill coefficients were small for the cases in which ED₅₀ was an outlier. Consequently, these values canceled each other out and drew a similar model, suggesting that fewer parameters than those used in the sigmoid E_max model would have been sufficient. Thus, the results of this analysis considered to be valid because the goodness-of-fit was not distorted, and the estimation did not collapse even in the model with an outlier ED₅₀.

Covariate analysis on the normalized dose-HbA1c model identified that canagliflozin showed more potent efficacy which was consistent with previous reports^17,18. However, our results further suggested that the stronger hypoglycemic trend with canagliflozin is due to the difference in the dose–response properties of the drug itself (a significantly greater E_max compared with those of the other drugs). Given that the selectivity of canagliflozin for SGLT2 is lower than that of other SGLT2is, the greater reduction in HbA1c with canagliflozin may be explained by inhibition of SGLT1 in the gastrointestinal tract²³. Although SGLT2 is preferentially expressed in the kidney, SGLT1 is more ubiquitously expressed in other organs including the small intestine, cardiac muscles, and skeletal muscles^24,25. Drug concentrations in the lumen of the gastrointestinal tract are often much higher than those in the plasma, and SGLT1/2 inhibition occurs via the extracellular domain of the transporter²⁶. Therefore, the greater HbA1c-lowering effect of canagliflozin may be associated with the inhibition of SGLT1 in the gastrointestinal lumen. Moreover, SGLT1 is also expressed in pancreatic α-cells; Suga et al. showed that canagliflozin, which inhibits SGLT1 if the drug concentration in the pancreas is high, may promote glucose-lowering effects via suppression of glucagon secretion from the pancreas²⁷. Studies that include less SGLT1/2 selective agents such as sotagliflozin may provide useful insights into this result. In contrast, although high SGLT2/SGLT1 selectivity is a desirable mechanism of glucose lowering efficacy, no differences in HbA1c reduction were observed between empagliflozin, the most SGLT2-selective drug and the other drugs.

Ipragliflozin also shows relatively low SGLT2 selectivity; however, no differences between ipragliflozin and other drugs were detected in this study. Although the reason for this result is unclear, it should be noted that most early and later clinical trials of ipragliflozin have been conducted at a somewhat lower dose range compared with its UGE (Figs. 3 and 4). Considering the UGE of other SGLT2is, it might be possible that ipragliflozin appeared a slightly higher effect than currently confirmed if the HbA1c lowering effect had been carefully evaluated at higher doses. Hence, these results suggest that the early adoption of a biomarker-based MBMA approach as carried out in this study may guide more efficient and evidence-based dose selection of the later clinical studies in future drug development.

Our analysis found that baseline HbA1c levels, body weight, disease duration, pretreatment, and renal function also affect the HbA1c-lowering effect of SGLT2is. DeFronzo et al. demonstrated excellent treatment effects in individuals with high baseline HbA1c levels, which is consistent with our results²⁸. In previous MBMAs of glucose-lowering agents, baseline HbA1c was incorporated into the model as a covariate^18,29. In addition, the glucose-lowering effect was smaller in individuals with a low GFR and poor renal function, which is consistent with studies showing that the effect of SGLT2is was attenuated with poor renal function³⁰. In contrast, canagliflozin was recently suggested to be nephroprotective in patients with chronic kidney disease in the CREDENCE study³¹. Dapagliflozin has also shown strong renoprotective effects in patients with stage 4 chronic kidney disease, with similar effects reported for other SGLT2is³². Such findings are expected to add to the benefits of renin–angiotensin–aldosterone system inhibitors³³.

The glucose-lowering effect was lower in patients with heavier body weights. There are currently no reports indicating that patient weight itself affects treatment effects. Patients who are obese may have higher insulin resistance, making it more difficult to lower their blood glucose levels, resulting in a difference in their glucose-lowering effects. Tofogliflozin and ipragliflozin, which have the shortest and longest half-lives, respectively, also showed no differences in HbA1c reduction.

A prolonged disease duration reduces therapeutic effects of glucose-lowering drugs³⁴, possibly because glycemic control weakens with advanced disease. The effect of disease duration on glucose-lowering efficacy was evaluated for ipragliflozin to explore the factors affecting HbA1c changes. The results showed that a high baseline HbA1c and short disease duration were associated with low HbA1c levels, a result consistent with this study³⁵.

Furthermore, inhibition of myocardial SGLT1, which is elevated in human ischemic heart disease, has recently been examined as a new target for the pharmacological effects of SGLT2is on cardiac diseases³⁶ and may be a new explanatory factor for canagliflozin and other SGLT1/2-inhibiting drugs. In addition, SGLT2 expression, which was previously undetectable in the heart, was found to be upregulated during myocardial infarction in mice, and empagliflozin prevented cardiovascular death³⁷. There has been a renewed focus on SGLT2 in the heart. The timing of SGLT2 expression detection in humans has not been uniformly analyzed based on the occurrence of ischemic events.

This study has some limitations. First, the MBMA in this study was designed and conducted in an exploratory manner and does not necessarily conform to existing reporting guidelines for systematic reviews, such as PRISMA³⁸. Second, we analyzed the relationship between UGE and the strength of the glucose-lowering effect but did not evaluate the frequency of side effects, long-term prognosis, or other aspects of drug treatment. We used the results of many studies to SGLT2is. Differences in the study designs may not be fully adjusted; thus the outcomes may have been influenced by these potential differences. Although summary statistics from randomized controlled trials are highly reliable, use of individual patient-level data may lead to more accurate analyses of covariates. Particularly, further studies are needed to investigate whether drugs with more potent SGLT1 inhibitory activity, such as sotagliflozin, have a different impact on its glucose-lowering effects.

Conclusion

The dose–response relationship of the six SGLT2is after dose normalization was similar, suggesting that glucose-lowering efficacy can be predicted by considering the normalized doses based on the UGE. This dose normalization approach allowed the HbA1c data from different SGLT2is to be integrated into the same model, which identified multiple covariates that could affect their glucose-lowering effects. Given the dosing regimen of SGLT2is for T2DM (most of which needs the adjustment of the dose according to patient symptoms), these findings could help physicians to determine the optimal drug for individual patients. Additionally, understanding of the mechanism of canagliflozin, which was identified as a covariate for the maximum effect of HbA1c lowering, is important for pursuing the detailed characteristics of SGLT2is. From the perspective of drug development, the same approach can be applied to other drug classes and may contribute to facilitating strategic and evidence-based dose selection for phase III trials.

Methods

Data collection

Data on UGE after a single administration of six SGLT2is in healthy participants in phase I studies were obtained from the summary of the regulatory application data for each drug^{19–21,39–41}. The application summaries were downloaded from the Pharmaceuticals and Medical Devices Agency website (https://www.pmda.go.jp/PmdaSearch/iyakuSearch/). The targeted trials and background information of participants are presented in Supplementary Table S1.

Phase II and III efficacy evaluation studies of the six SGLT2is in patients with type 2 diabetes were comprehensively collected from PubMed. PubMed search terms used to select trials for use in the MBMA are shown in Supplementary File 1.

The trials included in the analysis were at least 12 weeks in duration, and the HbA1c level was measured as an efficacy endpoint. From the literature, we obtained the mean and standard deviation of the change in HbA1c levels from baseline for each arm of trials. If no figures were available in the literature, data were obtained from ClinicalTrials.gov (https://clinicaltrials.gov/). In addition to the study design, including the number of participants, duration of treatment, and concomitant medications, we collected background information such as age, sex, and weight (Supplementary Table S2).

Dose normalization

The class effects of SGLT2is were analyzed using the MBMA based on the relationship between the dose and HbA1c change. However, because not all SGLT2is have the same pharmacokinetics, they do not elicit the same response at the same dose. Therefore, the dose was normalized. UGE was used as the normalization criterion because this pharmacological measure is directly related to the glucose-lowering effect (as reflected by HbA1c).

The following linear-logarithmic model was fitted to examine the relationship between the dose of each drug and UGE:

$$UGE=f_i\left(D,o,s,e\right)=a_i+b_i\ast {\text{log}}_{10}\left(D,o,s,e\right)$$ 1

where i indicates the type of drug, and a and b are the drug-specific model parameters. We chose the logarithmic linear model because a simple linear model was advantageous for the derivation of the reference UGE and the corresponding reference dose described below. We also tested other nonlinear models, including polynomial forms and the Emax model, but did not obtain meaningful improvements. This is supported by the results in Fig. 1, which show that the logarithmic linear model already adequately fits the data.

We then set the reference UGE as the normalization criterion. This value was calculated from the geometric mean of the UGE at the clinical dose of each drug (${\mathit{UGE}}_{clinical,i}$), according to Eq. 2. If more than one clinical dose was available for a drug, ${\mathit{UGE}}_{clinical,i}$ was calculated as the geometric mean of the UGE at those doses, as expressed in Eq. 3. In this equation, J is the number of clinical doses for the drug, and δ indicates the availability of the UGE data for each clinical dose (0: no data; 1: data available). This means that, if the clinical dose was not tested in phase I studies and the corresponding UGE was missing, it will be imputed by linear-logarithmic model prediction (i.e., open colored circles in Fig. 1).

$${\mathit{UGE}}_{\mathit{reference}}=\sqrt[I]{{\prod }_i{\mathit{UGE}}_{clinical,i}}$$ 2

$${\mathit{UGE}}_{clinical,i}=\sqrt[J]{{\prod }_j({\mathit{UGE}}_{clinical,i,j}{)}^{{\delta }_j}\ast {(f\left({\mathit{Dose}}_{i,j}\right))}^{1-{\delta }_j}}$$ 3

Finally, the reference UGE was substituted into the inverse function of the linear-logarithmic model to determine the reference dose of each drug. The normalized dose was obtained by dividing the actual dose by the reference dose.

$${\mathit{Dose}}_{reference,i}=f_i^{-1}\left({\mathit{UGE}}_{\mathit{reference}}\right)$$ 4

$${\mathit{Dose}}_{normalized,i}=\frac{{\mathit{Dose}}_i}{{\mathit{Dose}}_{reference,i}}$$ 5

To validate the above procedure, the relationship between Dose_normalized and UGE was fitted using Eq. 1 for all drugs. At this time, the UGE was set as the UGE_reference when Dose_normalized = 1.

MBMA for six SGLT2is

Based on the data collected from 83 studies on six drugs, model analysis to verify the relationship between the normalized dose and HbA1c change. The following sigmoid E_max model was used to describe the HbA1c changes:

$$Hb1acchange=Base+\frac{E_{\mathit{max}}\ast {[Dos{e}_{\mathit{normalized}}]}^n}{{\left[{\mathit{ED}}_{50}\right]}^n+{\left[D,o,s,e_{\mathit{normalized}}\right]}^n}+\frac{\mathit{SD}}{\sqrt{n_{\mathit{sub}}}}\ast \epsilon$$ 6

where Base: HbA1c change by placebo treatment; E_max: maximum treatment effect; ED₅₀: dose showing 50% E_max; n: Hill coefficient; SD: standard deviation of HbA1c change; n_sub: number of subjects in each arm. To account for the differences in the reliability between data, the standard deviation of the residual error (ε) was fixed at 1 and scaled by the standard error of the observed HbA1c change.

The error and covariate models for each parameter are expressed as follows:

$$Base={\theta }_1+\sum f\left(C,O,V\right)+{\eta }_1$$ 7

$$E_{\mathit{max}}={\theta }_2\times \prod f\left(C,O,V\right)\times \text{exp}\left({\eta }_2\right)$$ 8

$${\mathit{ED}}_{50}={\theta }_3$$ 9

$$\text{n}={\theta }_4$$ 10

where θ: population mean of the parameter; COV: covariate; and η: ISV that follows the normal distribution with mean 0 and variance ω². ISV was assumed only for Base and E_max.

To explain the ISV, covariate analysis was performed. See the configuration file (config.scm) attached in the supplements for details on tested covariate model structures. Candidate covariates includes baseline age, sex, weight, body mass index, duration of illness, fasting plasma glucose level, baseline HbA1c level, systolic and diastolic blood pressure, renal function, study duration, whether the study was conducted in Japan, prior treatment, concomitant medication, and drug type. Covariate selection was performed using the stepwise method, with the significance levels in the likelihood ratio test for forward inclusion and backward exclusion of 0.01 and 0.001, respectively.

Model validation

To validate the model, we created six types of goodness-of-fit plots (observations vs. population predictions, observations vs. individual predictions, square root of absolute value of CWRES vs. individual predictions, CWRES vs. normalized dose, histogram for CWRES and QQ plot). Additionally, we performed bootstrap analysis (500 samples).

Software

R and Rstudio were used for dose normalization, whereas NONMEM and Perl-speaks-NONMEM were used for MBMA. NONMEM was used in FOCE-I mode. The stepwise covariate selection was conducted using the scm command of the Perl-speaks-NONMEM, and bootstrap analysis was conducted using the bootstrap command. All reproducible codes are attached in the supplements.

Author contributions

AI, HY, HS and AH conceived the study; AI and HS wrote the initial draft; AI collected the data; AI, HY and RJ performed MBMA analyses; RJ prepared the figures and tables; HS, AI, HY, RJ, YS, and AH revised and approved the final draft.

Funding

Japan Society for the Promotion of Science (21K06797, 21K06797).

Data availability

Data and codes used in the analysis are provided in the supplements.

Declarations

Competing interests

Hideki Yoshioka and Akihiro Hisaka work for the Pharmaceuticals and Medical Devices Agency (Tokyo, Japan) at present, but the views expressed in this article are those of the authors and do not necessarily reflect the official views of the Pharmaceuticals and Medical Devices Agency. Yamato Sano is an employee of Pfizer R&D Japan. However, Pfizer R&D Japan is not involved in the analysis of this study. There is no conflict of interest to be disclosed for other authors.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-76256-6.